Gravitational Model of the Internal Structure of a Proton, an Electron, and a Neutron in General Relativity Theory

From the viewpoint of general relativity theory (GRT), the obstacles are discussed that do not allow gravitational and electromagnetic fields to be used to create a model of elementary particles and atomic nuclei, including vanishingly small gravitational interaction in comparison with electromagnetic one on microcosm scales, incomplete geometrizability of the electromagnetic field itself, its long-range action in comparison with short-range action of nuclear forces, and the Coulomb repulsion of likely charged protons in a nucleus (it seems so natural that it cannot provide focusing of nucleons and holding nuclei in a compact state) – all these phenomena are differently interpreted in GRT primarily due to universality of gravitational interaction that plays the dominant role at any micro- and macrocosm scales. Based on exact solution of the Einstein–Maxwell equations for a centrally symmetric free electromagnetic field and a dust-like substance, gravitational models of a proton, an electron, and a neutron are suggested in the form of pulsing unclosed wormholes with two static necks – electric charges of opposite signs – emerging into two parallel asymptotically flat vacuum spaces. The neutron is represented in the form of a double wormhole. The calculated radii are 0.8412 fm for the proton, 386.17 fm for the electron, and 1.0049 fm for the neutron. The proton radius coincides within 4% with its experimental value equal to 0.8409 fm measured from the Lamb shift of muon-hydrogen. The electron radius is 459 times greater than the proton radius. However, when the proton is scattered on the electron, its wormhole penetrates into the center of the electron wormhole, the curvature radius of its neck decreases down to the above-indicated neutron radius at the expense of a portion of the relativistic rotational proton energy and the energy of the curved space, that is, the energy of the gravitational field transferred to the electron.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    T. F. E. Kaluza, Zum Unitatsproblem in der Physik, Sitzungsber. Preuss. Akad. Wiss., Berlin, 1921.

    Google Scholar 

  2. 2.

    O. Klein, Z. Phys., 37, 895 (1926).

    ADS  Article  Google Scholar 

  3. 3.

    Yu. A. Khlestkov, L. A. Sukhanova, and N. S. Trushkin, Chin. J. Phys., 54, No. 4, 614–627 (2016).

    Article  Google Scholar 

  4. 4.

    L. A. Sukhanova and Yu. A. Khlestkov, Russ. Phys. J., 60, No. 7, 1156–1172 (2017).

    Article  Google Scholar 

  5. 5.

    Yu. A. Khlestkov and L. A. Sukhanova, Chin. J. Phys., 55, No. 5, 1794–1807 (2017).

    Article  Google Scholar 

  6. 6.

    Yu. A. Khlestkov, Zh. Eksp. Teor. Fiz., 128, No. 2, 300–311 (2005); arXiv:0807.3618 [gr-qc] (2008).

  7. 7.

    Y. A. Khlestkov and L. A. Sukhanova, Found. Phys., 46, No. 6, 668–688 (2016).

    ADS  MathSciNet  Article  Google Scholar 

  8. 8.

    H. Yukawa, Prog. Theor. Phys., 17, 48 (1935).

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to A. Yu. Khlestkov.

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 73–88, February, 2019.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Khlestkov, A.Y., Khlestkov, Y.A. Gravitational Model of the Internal Structure of a Proton, an Electron, and a Neutron in General Relativity Theory. Russ Phys J 62, 264–283 (2019). https://doi.org/10.1007/s11182-019-01709-9

Download citation

Keywords

  • wormholes
  • neck
  • charge
  • radius
  • geometrization
  • electron
  • proton
  • neutron
  • universality of gravitational interaction